In this paper, we tackle domain adaptation based HAR from a different perspective, and hence propose Substructural Domain Adaptation (SSDA) for accurate and robust domain adaptation. Generally speaking, Substructure describes the fine-grained latent distribution of data. For the entire class, it can be understood as a data cluster of the class.  REF  shows how SSDA performs substructure-level matching. Compared with the domain- and class-level methods, SSDA utilizes more fine-grained locality information to overcome under-adaptation.
In contrast to sample-level methods that can be easily affected by noise or outliers, SSDA utilizes the substructure of the data that can prevent over-adaptation.
Based on SSDA, we propose an optimal transport-based implementation, namely, Substructural Optimal Transport (SOT), for the cross-domain HAR problems.
OT [1]} has a solid theoretical background and allows a flexible mapping without being restricted to a particular hypothesis class [2]}, hence it has no restriction on the numbers of substructures in different domains.
Specifically, SOT first obtains the internal substructures by a clustering method. Then, the activity substructure weights of the source domain are given via partial optimal transport according to its distance from the target domain.
Finally, two representations of substructures are used to learn a transportation plan matching the probability distribution functions (PDFs) on both substructures.
We conduct experiments on four public activity recognition datasets (UCI DSADS [3]}, UCI-HAR [4]}, USC-HAD [5]}, and PAMAP2 [6]}). The results demonstrate that our method outperforms other state-of-the-art methods with a significant improvement of over \(\mathbf {9}\%\)  w.r.t classification accuracy, while it is \(\mathbf {5} \times \)  faster than traditional OT-based DA methods with the same hyper-parameters.
